Convert the following into engineering notation 9.423×10 to the fifth power
The Correct Answer and Explanation is:
Engineering Notation of 9.423 × 10^5
To express the number (9.423 \times 10^5) in engineering notation, we need to adjust it so that the exponent of the power of ten is a multiple of three. This form is useful in engineering as it makes it easier to read and compare values that differ by several orders of magnitude.
Step-by-Step Conversion:
- Identify the Current Format:
The given number is in scientific notation, where (9.423) is the coefficient and (10^5) is the power of ten. - Determine the Exponent:
The exponent here is (5). For engineering notation, we want this exponent to be a multiple of three. The closest multiple of three that is less than or equal to (5) is (3). - Adjust the Coefficient and Exponent:
To convert from (10^5) to (10^3), we can express the number as:
[
9.423 \times 10^5 = 9.423 \times 10^{5-3} \times 10^3 = 9.423 \times 10^2 \times 10^3
]
This simplifies to:
[
9.423 \times 10^5 = 94.23 \times 10^4
] - Final Result:
The result in engineering notation is (94.23 \times 10^4).
Conclusion:
Engineering notation is primarily used in fields like electrical engineering, where it provides clarity when working with very large or very small numbers, as it keeps the exponent in manageable ranges. By using a coefficient that ranges from (1) to (999) and an exponent that is a multiple of three, engineers can quickly grasp the scale of a number without performing extensive calculations. Thus, the engineering notation for (9.423 \times 10^5) is (94.23 \times 10^4), which is now properly formatted for practical use in engineering calculations.